Natural units

Definitions of speed of light, reduced Planck's constant, and electronvolt in terms of kilograms, meters, seconds:

$c=299792458\frac{m}{s}$

$\hslash =1.054571817\times 10^{-34}kg\frac{m^2}{s}$

$eV=1.602176463\times 10^{-19}kg\frac{m^2}{s^2}$

Then solve for second:

$\frac{\hslash }{eV}=6.582120268\times 10^{-16}s$

$s=1.519267287\times 10^{15}\frac{\hslash }{eV}$

Solve for kilogram:

$c^2=8.987551787\times 10^{16}\frac{m^2}{s^2}$

$\frac{eV}{c^2}=1.782661731\times 10^{-36}kg$

$kg=5.609589202\times 10^{35}\frac{eV}{c^2}$

Solve for meter:

$\frac{\hslash }{c}=3.51767294\times 10^{-43}kg\cdot m$

$\frac{\hslash }{c}=1.973270014\times 10^{-7}\frac{eV}{c^2}m$

$5067730.179\frac{\hslash }{c}\frac{c^2}{eV}=m$

$m=5067730.179\frac{\hslash c}{eV}$

Summarize results:

$kg=5.609589202\times 10^{35}\frac{eV}{c^2}$

$m=5067730.179\frac{\hslash c}{eV}$

$s=1.519267287\times 10^{15}\frac{\hslash }{eV}$

Dimensional conversion: $k{g}^x{m}^y{s}^z\sim c^{y-2x}{\hslash }^{y+z}e{V}^{x-y-z}$

Now omit c and ℏ:

$kg=5.609589202\times 10^{35}eV$

$m=5,067,730.179\frac{1}{eV}$

$s=1.519267287\times 10^{15}\frac{1}{eV}$

Dimensional conversion: $k{g}^x{m}^y{s}^z\sim e{V}^{x-y-z}$

Based on: http://www.physics.gla.ac.uk/~dmiller/lectures/RQM_2008.pdf, page 12